Parmentier rhymes with:
carpentier, carpentier, mintier, altier, carpentier, cartier, chartier, cloutier, cottier, courtier, dirtier, emptier, flightier, fortier, gautier, heartier, heftier, loftier, meatier, meteor, mightier, mintier, mortier, nastier, palmatier, peltier, portier, potier, prettier, rustier, saltier, sportier, tastier, thriftier, trottier, whittier
Parmentier sounds like:
parameter, parmenter, parmeter, perimeter, permenter, premature, premonitory, printer, promoter